A topological transition of graphen oberved in a microwaves experiment and published in Physical Review Letters

Graphene, a two-dimensional crystal of carbon, is undoubtedly the “super-material” of the twenty-first century. Thanks to its unique properties (mechanical, thermal, electrical and optical), it allows to revisit basic concepts of condensed-matter physics and authorizes the boldest proposals in applications. A new and promising field of studies is currently investigated : to manipulate the structure of graphene to modify its properties, particularly electronic conduction. To deform the graphene to make it even better ! Before its implementation in components, researchers need to test this concept on artificial materials more easily controllable than real graphene. Thus, physicists from the Laboratoire de Physique de la Matière Condensée, in Nice, and the Laboratoire de Physique des Solides, in Orsay, have substituted the electron transport in the periodic potential created by carbon atoms by microwave transport through an honeycomb lattice made with dielectric cylindrical resonators. By applying a homogeneous compression to the lattice, they observe (i) a (topological) phase transition from a semi-metallic to an insulating phase ; (ii) the concomitant appearance of exotic states at the edges of the system.

The experimental set-up developed in Nice allows a perfect control of the lattice formed by the cylinders with centimetric diameter and height, the distance between neighboring resonators setting the intensity of the electromagnetic coupling. The configuration of the edges of the system, known to play a dominant role in transport, is especially important to control. In the study published in the journal Physical Review Letters, the initial system takes the form of a hexagon with smooth edges (edges called "armchairs") on its 6 edges. The density of states of this photonic graphene exhibits a conical structure in the vicinity of a "Dirac point". The experimental device allows to measure, for each of the allowable frequencies, the spatial distribution of the microwave field. In the initial situation, no particular concentration of energy at the edges is observed : there is no “edge states”. When compression along one of the crystal axes is performed, the density of states near the Dirac point changes its nature, and beyond a critical compression, a gap in the frequency appears. The deformation also leads to states localized atthe edges that intersect the axis of compression, the concentration of energy at the edges increasing with the compression.

Researchers are moving now, at one hand on a thorough study of edge states for more complex contours. On the other hand, achieving a compression variable in space, they try to simulate the action of a pseudo-magnetic field and, then, to demonstrate the appearance of Landau levels.

Figure caption : Experimental measurement of the intensity distribution of the electric field at the Dirac frequency (scale from white (minimum) to red (max.)) in a structure of graphene compressed. Electromagnetic energy is concentrated in this case at the edges.